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NR

Syntax

NR(X:POLY,L:LIST of POLY):POLY
NR(X:VECTOR,L:LIST of VECTOR):VECTOR
    

Summary

normal reduction

Description

This function returns the normal remainder of X with respect to L, i.e., it returns the remainder from the division algorithm. To get both the quotients and the remainder, use DivAlg. Note that if the list does not form a Groebner basis, the remainder may not be zero even if X is in the ideal or module generated by L (use GenRepr or NF instead).

example

    
Use R::= Q[xyz];
F := x^2y+xy^2+y^2;
NR(F,[xy-1,y^2-1]);
x + y + 1
-------------------------------
V := Vector(x^2+y^2+z^2,xyz);
NR(V,[Vector(x,y),Vector(y,z),Vector(z,x)]);
Vector(z^2, z^3 - yz - z^2)
-------------------------------
        
    

See Also